{
 "cells": [
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import plotly.figure_factory as ff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "trees = pd.read_csv('data/black_spruce.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "def jitter(data, amt=0.2):\n",
    "    return data + amt * (np.random.rand(len(data)) - 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Classification\n",
    "\n",
    "We'd like to create a model that explains the susceptibility of trees to windthrow. In other words, we need to build a model for a two-level nominal feature: fallen or standing. When the response variable is nominal, this modeling task is called *classification*. In this case there are only two levels, so this task is more specifically called *binary classification*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Constant Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by considering the simplest model: a constant model that always predicts one class. We use $ C $ to denote the constant model's prediction. For our windthrow dataset, this model will predict either $ C = \\text{standing} $ or $ C = \\text{fallen} $ for every input."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In classification, we want to track how often our model predicts the correct category. For now, we do this simply: we use a count of the correct predictions. This is sometimes called the *zero-one error* because the loss function takes on one of two possible values: 1 when an incorrect prediction is made and 0 for a correct prediction. For a given observed outcome $ y_i $ and prediction $ C $, we can express this loss function as follows:\n",
    "\n",
    "$$\n",
    "\\begin{aligned} \n",
    "{\\ell}(C, y) = \n",
    "\\begin{cases} 0 &  &\\text{when } C \\text{ matches } y\\\\ \n",
    "       1 &  & \\text{when } C \\text{ is a mismatch for }y\n",
    "\\end{cases}\n",
    "\\end{aligned} \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we have collected data, $\\mathbf{y} = [y_1 , \\ldots, y_n] $, then the average loss is:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "L(C, \\mathbf{y}) &= \\frac{1}{n} \\sum_{i=1}^n {\\ell}(C, y) \\\\\n",
    "  &= \\frac{\\# \\text{ mismatches}}{n} \n",
    "\\end{aligned}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the constant model (see {numref}`Chapter %s <ch:modeling>`), the model minimizes the loss when $ C $ is set to the most prevalent category."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case of the black spruce, we have the following proportions of standing and fallen trees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "status\n",
       "standing    0.65\n",
       "fallen      0.35\n",
       "Name: count, dtype: float64"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trees['status'].value_counts() / len(trees)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So our prediction is that a tree stands, and the average loss for our dataset is $0.35$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That said, this prediction is not particularly helpful or insightful. For example, in our EDA of the trees dataset, we saw that the size of the tree is correlated with whether the tree stands or falls. Ideally, we could incorporate this information into the model, but the constant model doesn't let us do this. Let's build some intuition for how we can incorporate predictors into our model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examining the Relationship Between Size and Windthrow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to take a closer look at how tree size is related to windthrow.\n",
    "For convenience, we transform the nominal windthrow feature into a 0-1 numeric feature where 1 stands for a fallen tree and 0 for standing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>diameter</th>\n",
       "      <th>storm</th>\n",
       "      <th>status</th>\n",
       "      <th>status_0_1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.02</td>\n",
       "      <td>standing</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11.0</td>\n",
       "      <td>0.03</td>\n",
       "      <td>standing</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.03</td>\n",
       "      <td>standing</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>656</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.94</td>\n",
       "      <td>fallen</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>657</th>\n",
       "      <td>17.0</td>\n",
       "      <td>0.94</td>\n",
       "      <td>fallen</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>658</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.98</td>\n",
       "      <td>fallen</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>659 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     diameter  storm    status  status_0_1\n",
       "0         9.0   0.02  standing           0\n",
       "1        11.0   0.03  standing           0\n",
       "2         9.0   0.03  standing           0\n",
       "..        ...    ...       ...         ...\n",
       "656       9.0   0.94    fallen           1\n",
       "657      17.0   0.94    fallen           1\n",
       "658       8.0   0.98    fallen           1\n",
       "\n",
       "[659 rows x 4 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trees['status_0_1'] = (trees['status'] == 'fallen').astype(int)\n",
    "trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This representation is useful in many ways. For example, the average of `status_0_1` is the proportion of fallen trees in the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion of fallen black spruce: 0.35\n"
     ]
    }
   ],
   "source": [
    "pr_fallen = np.mean(trees['status_0_1'])\n",
    "print(f\"Proportion of fallen black spruce: {pr_fallen:0.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having this 0-1 feature also lets us make a plot to show the relationship between tree diameter and windthrow. This is analogous to our process for linear regression, where we make scatterplots of the outcome variable against explanatory variable(s) (see {numref}`Chapter %s <ch:linear>`).\n",
    "\n",
    "Here we plot the tree status against the diameter, but we add a small amount of random noise to the status to help us see the density of 0 and 1 values at each diameter. As before, we jitter the diameter values too and adjust the opacity of the markers to reduce overplotting. We also add a horizontal line at the proportion of fallen trees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-04-02T16:07:17.773256Z",
     "start_time": "2018-04-02T16:07:17.757563Z"
    },
    "tags": [
     "hide-input"
    ]
   },
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   ],
   "source": [
    "fig = px.scatter(x=jitter(trees['diameter'], amt=0.5), \n",
    "                 y = jitter(trees['status_0_1']), \n",
    "                 log_x=True, width=450, height=250)\n",
    "\n",
    "fig.update_traces(marker=dict(opacity=0.5, size=5))\n",
    "fig.add_hline(y=pr_fallen, line_width=3, line_dash=\"dash\", line_color=\"black\")\n",
    "fig.update_layout(xaxis_title=\"Tree diameter (cm)\",\n",
    "                  yaxis_title=\"0 = standing,     1 = fallen\")\n",
    "\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This scatter plot shows that the smaller trees are more likely to be standing than the larger trees. Notice that the average status for trees (0.35) essentially fits a constant model to the response variable. If we consider that tree diameter as an explanatory feature, we should be able to improve the model.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A starting place might be to compute the proportion of fallen trees for different diameters. The following block of code divides tree diameter into intervals and computes the proportion of fallen trees in each bin:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "splits = [4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 25, 32]\n",
    "tree_bins = (\n",
    "    trees[\"status_0_1\"]\n",
    "    .groupby(pd.cut(trees[\"diameter\"], splits))\n",
    "    .agg([\"mean\", \"count\"])\n",
    "    .rename(columns={\"mean\": \"proportion\"})\n",
    "    .assign(diameter=lambda df: [i.right for i in df.index])\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot these proportions against tree diameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "hide-input"
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            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "white",
            "gridcolor": "rgb(232,232,232)",
            "gridwidth": 2,
            "linecolor": "rgb(36,36,36)",
            "showbackground": true,
            "showgrid": false,
            "showline": true,
            "ticks": "outside",
            "zeroline": false,
            "zerolinecolor": "rgb(36,36,36)"
           },
           "yaxis": {
            "backgroundcolor": "white",
            "gridcolor": "rgb(232,232,232)",
            "gridwidth": 2,
            "linecolor": "rgb(36,36,36)",
            "showbackground": true,
            "showgrid": false,
            "showline": true,
            "ticks": "outside",
            "zeroline": false,
            "zerolinecolor": "rgb(36,36,36)"
           },
           "zaxis": {
            "backgroundcolor": "white",
            "gridcolor": "rgb(232,232,232)",
            "gridwidth": 2,
            "linecolor": "rgb(36,36,36)",
            "showbackground": true,
            "showgrid": false,
            "showline": true,
            "ticks": "outside",
            "zeroline": false,
            "zerolinecolor": "rgb(36,36,36)"
           }
          },
          "shapedefaults": {
           "fillcolor": "black",
           "line": {
            "width": 0
           },
           "opacity": 0.3
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           },
           "baxis": {
            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           },
           "bgcolor": "white",
           "caxis": {
            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           }
          },
          "title": {
           "x": 0.5,
           "xanchor": "center"
          },
          "width": 350,
          "xaxis": {
           "automargin": true,
           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
           "showline": true,
           "ticks": "outside",
           "title": {
            "standoff": 15
           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
           "showline": true,
           "ticks": "outside",
           "title": {
            "standoff": 15
           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
          }
         }
        },
        "width": 450,
        "xaxis": {
         "anchor": "y",
         "autorange": true,
         "domain": [
          0,
          1
         ],
         "range": [
          0.6130538244904317,
          1.5626667769759242
         ],
         "title": {
          "text": "Tree diameter (cm)"
         },
         "type": "log"
        },
        "yaxis": {
         "anchor": "x",
         "domain": [
          0,
          1
         ],
         "range": [
          0,
          1
         ],
         "title": {
          "text": "Proportion down"
         },
         "type": "linear"
        }
       }
      },
      "image/png": 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   ],
   "source": [
    "fig = px.scatter(tree_bins, x='diameter', y='proportion', size='count',\n",
    "                 log_x=True, \n",
    "                 labels={'diameter':\"Tree diameter (cm)\",\n",
    "                         'proportion':\"Proportion down\"},\n",
    "                 width=450, height=250)\n",
    "\n",
    "fig.update_layout(yaxis_range=[0, 1])\n",
    "fig.show()"
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    "The size of the markers reflects the number of trees in the diameter bin. We can use these proportions to improve our model. For example, for a tree that is 6 cm in diameter, we would classify it as standing, whereas for a 20 cm tree, our classification would be fallen. A natural starting place for binary classification is to model the observed proportions and then use these proportions to classify. Next, we develop a model for these proportions."
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   "source": []
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